相关论文: Parallelism Structure on a Smooth Manifold

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…

In this article we investigate some properties of equivariant embeddings of a symmetric K\"ahlerian manifold. Motivated by a theorem of Cartan and Wallach on equivariant embeddings of symmetric spaces we characterize these embeddings in the…

The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint…

Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…

In this continuation of \cite{BDS}, we investigate the deformations of holomorphic Cartan geometries where the underlying complex manifold is allowed to move. The space of infinitesimal deformations of a flat holomorphic Cartan geometry is…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously…

For a general affine connection with parallel torsion and curvature, we show that a post-Lie algebra structure exists on its space of vector fields, generalizing previous results for flat connections. However, for non-flat connections, the…

We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…

In this paper we study the autoparallelity w.r.t. the e-connection for an information-geometric structure called the SLD structure, which consists of a Riemannian metric and mutually dual e- and m-connections, induced on the manifold of…

First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on…

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion…

We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic…

There are two methods to study families of conformal theories in the operator formalism. In the first method we begin with a theory and a family of deformed theories is defined in the state space of the original theory. In the other there…

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…

Cartan geometry provides a unifying algebraic construction of curvature and torsion, based on an underlying model Lie algebra -- a viewpoint that can be extended naturally to the higher algebraic structures underlying supergravity. We…

Co-Euler structures were studied by Burghelea and Haller on closed manifolds as dual objects to Euler structures. We extend the notion of co-Euler structures to the situation of compact manifolds with boundary. As an application, by…

In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…

Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…